Density depletion profile and solvation free energy of a colloidal particle in a polymer solution

Abstract

The solvation free energy and polymer density depletion profile of a single mesoscopic colloidal particle in a solution of free nonadsorbing polymer chains are investigated theoretically. Keeping both the particle to polymer size ratio and the degree of inter-chain overlap arbitrary, we see how the qualitatively different behavior evolves in the limits of small and large size ratios and of dilute and semidilute solutions. While most of our results are obtained within a mean-field approach, we also use a “renormalized tree approximation” to estimate the surface tension and the coefficient of spontaneous curvature in a Helfrich expansion for large particle to polymer size ratio. There is a weak maximum in the polymer density profile for arbitrary size ratio. For small size ratio the maximum can be explained in terms of a minimum in the bulk polymer density correlation function.